Become a paramedic only if you want to make it your career. Paramedic school offers an algorithmic "cookbook" method of treating patients that is very different from a physician's practice of medicine. If you want to be a doctor you are better off taking science classes instead, or becoming a basic EMT.
With that said, working as a paramedic HAS benefitted me more than I was expecting, but not in some earth-shattering way that places me well ahead of my peers. My paramedic classes only scratched the surface of the physiology I've learned in med school so far, so that part was only helpful as basic background info. Like the first poster, it has definitely helped make patient assessments go more smoothly and helped me build rapport with patients. I noticed the biggest boost with some of the practical content:
-Interpreting basic ECGs and 12-leads
-Cardiac drugs (ACLS is never going away!)
-Identification and treatment of major, common illnesses: CHF, asthma, COPD, chronic bronchitis, etc.
-Psych/neuro disorders and treatment
-Types of head/brain injuries
-IV starts and first aid skills
-Formulating treatment plans for standardized (fake) patients
-Confidence with presenting patient cases to a preceptor
As for learning drugs and physical exams, those were definitely made easier but taught me that I still have A LOT to learn. The EMT-P curriculum taught me when to give a drug but not WHY to give a drug or how it actually works in the body. The neuro exam I had learned was a joke. There is a huge overall knowledge gap that med school will fill. The two fields are related, but it's not worth the time or expense if med school is your goal.